If you start from the right assumptions you can logically justify just about anything.
Proof that life is worth living:Lemma: We must show a human life is not wasteful.
Assumption1: Time is infinite denoted T
Assumption2: Human life expectancy is finite denoted H
Since infinity minus a finite constant is infinity we note that T - H = T
Therefore the amount of time a human spends dead is unaffected by the decision to continue living.
We conclude a human life is not wasteful.
Proof: We must show life is worth living.
Assumption3: The quality of existence is defined as the summation of the absolute values of all experiences. Let Q denote the total quality of existence in a human life.
Q = |e1| + |e2| +|e3|+ ...+|en|
where e1 is experience 1 and n is the number of experiences in a human's life.
Assumption4: The quality of existence without consciousness is 0.
Assumption5: A quality of existence at 0 is the most undesirable level of quality.
As the time of a human life moves from 0 to H, a human will accumulate a number of experiences, each experience bringing Q to a greater value.
|e1| < |e1|+|e2| < |e1|+|e2|+|e3|<...< |e1|+|e2|+|e3|+...+|en| where n represents the number of experiences in a human's life.
By our lemma, since a human life is not wasteful a human ought to live as long as possible to accumulate as many experiences as possible to raise quality of life Q.
We conclude by saying that all the experiences a human has through their first steps, the emotional ties they have with one another, intellectual stimulation, and the purposeful experience of assisting others makes life worth living.